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Streamflow Trends in Switzerland
Project Work
by
Kevin Mersch
E-mail: [email protected]
05.12.2011
Supervisor: Dr. P. Molnar
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26.04.10 / NB
Beiblatt zu jeder an der ETH Zrich verfassten schriftlichen Arbeit
Ich erklre mit meiner Unterschrift, das Merkblatt Plagiat(vgl. http://www.ethz.ch/students/semester/plagiarism_s_de.pdf) zur Kenntnis genommen, dievorliegende Arbeit selbstndig verfasst und die im betroffenen Fachgebiet blichen Zitiervorschrifteneingehalten zu haben.
Supervisor ___________________ ____________________________________
Studierender ___________________ ____________________________________
Ort, Datum ___________________ Unterschrift __________________________
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3 Streamflow Trends in Switzerland
Abstract
Mean daily streamflow records from 39 watersheds in Switzerland with a mostlyundisturbed runoff regime are analysed for trends with the MannKendall non-
parametric test in three study periods (1970-1990, 1980-2000, 1990-2010). Thestatistical significance of trends is tested for each station on a seasonal basisand for different streamflow quantiles at a 10% significance level. Identifiedtrends in streamflow are examined and correlated with watershed attributes.
Complex changes in the streamflow regime in Switzerland especially in themore recent periods have been identified, especially in autumn and winter.Particularly the most recent period (1990-2010) experiences a considerable shiftfrom high towards low flows for every quantile in autumn and winter. Theincreasing trend of spring flows is experiencing a decaying development overthe three analysed periods. Summer flows exhibit a decreasing trend, especiallyin magnitude. Behaviour in the summer period is different, indicating both
upward and downward trends. Substantial differences in trends depending onmean basin altitude couldnt be identified for any season but summer, wherestations located between 1000m and 2000m experience increasing trends whichstand in opposition to stations from higher or lower elevations. Winter medianflow of watersheds without glacier remain unchanged, while basins with glaciersface downward trends.
Correlation between mean watershed elevation and trends is strongly depen-dent on season and quantile. Correlation analyses reveal moderate relationshipsbetween streamflow trends and mean basin elevation and glacier coverage. Au-tumn and summer show negative correlation for low flows, resp. moderateflows. In winter high flows show a good correlation with magnitude of trend.
Trends are present in every period for high and low flows. Magnitude de-pends on period and season of interest. Results suggest that, regardless of thetype of environment of watersheds, all basins are subject to streamflow change,specifically in the last 20 years.
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Contents
1. Introduction 6
2. Data 8
3. Methods 11
3.1. Mann-Kendall nonparametric trend test . . . . . . . . . . . . . . . . . . . . 113.2. Theil-Sen slope estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3. Spearman rank correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4. Results 14
4.1. Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2. Differences in altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3. Correlation with basin attributes . . . . . . . . . . . . . . . . . . . . . . . . 214.4. Open Quetions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5. Conclusions 23
6. Acknowledgements 25
Literature 26
A. Appendix A 27
A.1. Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27A.1.1. Basin Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
A.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31A.2.1. Slope estimate results . . . . . . . . . . . . . . . . . . . . . . . . . . 31
A.2.2. Mann-Kendall relative frequency results . . . . . . . . . . . . . . . . 33A.2.3. Altitude groups results . . . . . . . . . . . . . . . . . . . . . . . . . . 35A.2.4. Glacier cover results . . . . . . . . . . . . . . . . . . . . . . . . . . . 39A.2.5. Spearman rank correlation results . . . . . . . . . . . . . . . . . . . 42
A.3. Additional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
B. Appendix B 50
B.1. Main Matlab Program for Mann-Kendall Theil-Sen . . . . . . . . . . . . . 50B.2. Main Matlab Program for Representative Discharge . . . . . . . . . . . . . 53
List of Figures
1. Representative Discharge [mm/season] for all season of q50 streamflow av-eraged over all stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
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2. Representative discharge [mm/year] for all season of q50 streamflow averagedover all stations and grouped by station altitude. . . . . . . . . . . . . . . . 10
3. Relative frequencies of high( +) and low(-) flows over all stations for allquantiles and for every period. . . . . . . . . . . . . . . . . . . . . . . . . . 15
4. Slope estimate for all quantiles and for every period. . . . . . . . . . . . . . 165. Slope estimate [mm/season] and standard deviation for 50- and 90-percent
quantiles grouped according to altitude for the period 1990-2010. . . . . . 186. Relative frequencies for 50- and 90-percent quantiles grouped according to
altitude for the period 1990-2010. . . . . . . . . . . . . . . . . . . . . . . . 197. Relative frequencies for 50- and 90-percent quantiles grouped according to
glacier cover for the period 1990-2010. . . . . . . . . . . . . . . . . . . . . . 208. Spearman rank correlation coefficients for mean basin altitude and estimated
slope (a) and MK Z statistic (b) . . . . . . . . . . . . . . . . . . . . . . . . 219. Representative Discharge [mm/season] for all season of q90 streamflow av-
eraged over all stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
10. Representative discharge [mm/year] for all season of q90 streamflow averagedover all stations and grouped by station altitude. . . . . . . . . . . . . . . . 47
11. Estimated slopes [mm/season] and standard deviation for 50- and 90-percentquantiles grouped according to glacier cover for the period 1990-2010. . . . 48
12. Spearman rank correlation coefficients of relative glacier cover and estimatedslope (a) and MK Z statistic (b) . . . . . . . . . . . . . . . . . . . . . . . . 49
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6 Streamflow Trends in Switzerland
1. Introduction
Trend detection in records of hydroclimatic variables (e.g. air temperature, precipitation,streamflow) contributes significantly to the on-going debate on climate change. So far
the focus of research was on temperature and precipitation rather than on streamflow,giving reason to investigate the latter variable more closely. Records show general increaseof temperature (and precipitation) [(M. Beniston u. Marinucci, 1994)], which have beenrelated to climate change effects. The question arises, if these trends can also (already) bedetected in streamflow data and again, if these trends can be related to climate change. Itis still not clear if and how changes in air temperature and precipitation manifests itself instreamflow. Before this can be investigated, it is first necessary to analyse how streamflowregimes have changed. From the water resources management perspective persisting trendsin streamflow are great importance, particularly trends of extreme events.
Below in figure 1 a representative chart on runoff over the last forty years is shown. Atrend is not obviously detectable with the bear eye; so statistical tools need to be considered
to get a more predicative picture. What can be noticed clearly is the high variation in runoffmagnitude from one season to the other.
Figure 1: Representative Discharge [mm/season] for all season of q50 streamflow averagedover all stations.
The big difference between temperature, precipitation and streamflow is that streamflowis an integrated variable over a watershed. This means that the influence of the first twohydroclimatic variables, which are both point measurements, should to a certain degree be
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noticeable in the integrated value, namely streamflow. Further disadvantage of the firsttwo variables is the high spatial and temporal variability, which can hamper detection ofregional trends.
Switzerland covers an area of 41,284 km2 of which about two thirds is forest and agri-
cultural land. Altitude ranges from 193 m (Lago Maggiore) to 4,634 m (Monte Rosa) andmean annual precipitation reaches about 1480 mm while mean annual runoff is about 960mm (Hydrological Atlas of Switzerland, 19611980). In terms of water resources, 63% ofthe surface water supplies are stored in natural lakes, 35% in glaciers and the remaining2% in artificial lakes. Switzerland lies in four large European watersheds: the Rhine River,draining into the North Sea, the Rhone and Po Rivers, draining into the MediterraneanSea, and the Inn which eventually drains into the Black Sea.
The data and methods are described in Section 2 and 3. Section 4 lists the main resultsaccording to the goals of this project work: first observed streamflow trends are investi-gated, then a correlation analysis between watershed attributes and observed streamflow
trends is conducted. Last some open questions are identified. Finally, the main conclusionsare summarized in Section 5.
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2. Data
Data sources
The analysis of streamflow trends is conducted with data from 39 stations spread aroundthe whole of Switzerland. All these stations provide records of mean daily streamflow rang-ing from 1970 to 2010. More stations were available depending on the period of analysis(52 in total). However, to be consistent in calculations, only stations that provided recordsover the whole of the above-mentioned period were considered. As former trend analysisof streamflow show, trend significance is strongly dependent on flow magnitude and thusseason [Pavel Ya. Groisman u. Karl (2001), (D. P. Lettenmaier, 1991)]. Considering thefacts on Switzerland mentioned in the previous section, snow and ice melt are importantcontributors to runoff seasonality. Streamflow trend analysis on an annual basis mightconceal important information through averaging compared to a seasonal basis [M. Benis-ton u. Marinucci (1994), M.-V. Birsan (2005)]. Hence, seasonality was taken into accountby defining four climatological seasons and analysing them separately (Spring, Summer,Autumn, Winter):
Table 1: Definition of season division
Season Months nr of Days
Spring March - May 92Summer June - August 92Autumn September - November 91
Winter December - January 90
After this, daily streamflows were not analysed directly, but data records were split into
3 periods of each 20 years with 10 overlapping years. This length of period seems to beadequate to capture trends without getting too much variability, which could complicateinterpretation. In this project work shifts in the distribution of daily data are of interest,so the test is applied to quantiles determined at the seasonal timescale. The deciles ofstreamflows as well as minimum and maximum runoff were computed to minimise dataload without losing to much representatitivity. The seasonal qquantile xq(i) of the meandaily flow X is obtained for every season (year) i as the value for which P r(X < x) = q.For instance, the q20-value of a station is the runoff for which 20% of all mean daily flowsfor the given season are below this value. To sum up, in order to identify shifts in thedistribution of mean daily streamflow, a range of 11 quantiles on seasonal bases ( qMIN,qMAX, and q10, q20...q90) were studied for three different observation periods. The analy-sis methods are standard: Mean daily runoff is analysed for trends with the MannKendallnonparametric trend test and the TheilSen slope estimator (both presented in the nextsection).
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Streamflow data used in this work were high resolution records of mean daily discharge.The three main criteria for station selection [M.-V. Birsan (2005)] were:
no substantial influence by water withdrawals for hydropower or other water-usepurposes
spatial independence between station records at least 30 years of continuous and complete observations
Spatial independence for stations located along the same river was ensured by alwayschoosing the upstream station. This offers a good compromise between the assumed in-dependence of station records and a relatively high number of stations [(M.-V. Birsan,2005)].
Alititude groups
In Switzerland 52% of its area lies above 1000 m.a.s.l. and 23% above 2000 m. Froma hydrological perspective, Switzerland can be divided into three distinct runoff regimestypes: Alpine, Midland-Jura, and Southern Alpine (Aschwanden (1985)). So, to get amore detailed picture, the stations were grouped according to the mean altitude of thecorresponding basin, so that they could be compared among each other. Furthermore,the groups were also compared to trends observed by computing all available stations. Inappendix A.1.1 basin attributes and number of stations for each group are listed. For theperiod from 1990-2010 differences according to station altitude were analysed in terms ofslope estimate and relative frequency. To lower data load only two runoff quantiles werelooked at, namely q50 and q90.
Glacier cover
In addition to grouping stations by elevation, they are also divide into a group whichpresent glacier cover and a group which doesnt. Surely both attributes are quite similarand correlated to certain extent. This classification will likely reveal interesting facts,as basins that have an Alpine influence reach a maximum seasonal runoff in spring andsummer. This analysis shall also only consider the 2 quantiles used in the altitude groupsfrom year 1990 to 2010.
Figure 2 shows the same runoff data as figure 1, but with gauging stations groupedaccording to the mean elevation of the corresponding watershed. It highlights that thediffences in flow magnitude related to seasonality is strongly dependent on altitude. Therunoff from basins above 2000m fluctuates considerably compared to the other those oflower stations.
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Figure 2: Representative discharge [mm/year] for all season of q50 streamflow averagedover all stations and grouped by station altitude.
.
For altitude, three groups were formed (0-1000m, 1000-2000m and >2000m), and forglacier cover only two (not glacier covered and partly glacier covered). Neither precipitationnor temperature data were considered, as this work should focus only on the output of therainfall runoff system. Another reason is the relative abundance of assessments on theseparticular values compared to runoff data. (Representative discharge of the q90 streamflow
can be found in appendix A.3).
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3. Methods
Two different statistical tools were used to analyse if streamflow data presented any trends.First, nonparametric slope estimation was used to get an idea of the magnitude of trends
throughout the time series. Also, the Mann-Kendall nonparametric trend test was em-ployed to give the estimated slopes a statistical significance. Simple but robust anddistribution-free tools were preferred. As serial correlation was mostly avoided by dividingdata according to seasons, no pre-whitening was applied to data to discriminate trendsfrom stochastic fluctuations and the influence of serial correlation.
3.1. Mann-Kendall nonparametric trend test
Trend analysis in this project work was conducted with the nonparametric Mann-Kendall(MK) test. This test has been widely used in hydrological studies. It is distribution-free,robust against outliers, and has a higher power than many other commonly used tests[Hess (2001)]. The test, suitable for non-normally distributed data with non-linear trends,should be applied to uncorrelated data [Helsel u. Hirsch (2002)]. Computation of the MKtrend test statistic Z and the identification of statistically significant trends are explainedhereafter. The MK test is applied to time series ofxq(i) with q = 0.1, 0.2,..., 0.9; and alsoto the seasonal minimum xmin(i) and maximum xmax(i), where i = 1,...,n years. Statis-tically significant trends are generally reported at the 10% significance level ( Z/2 = 0.1,two-tailed test). In this study the same significance level will be used to minimize typeII errors. The null and the alternative hypothesis of the MK test for trend in the randomvariable x are:
H0 : P r(xj > xi) = 0.5, j > i,HA : P r(xj > xi)
= 0.5, (twosided test)
The Mann-Kendall statistic S is calculated as
S =n1k=1
nj=k+1
sgn(xj xk) (1)
where xj and xk are the data values in years j and k, respectively, with j > k. sgn() isthe sign function:
sgn(x) =
1, if xj xk > 00, if xj xk = 0
1, if xj xk < 0(2)
Under the null hypothesis the distribution of S can be approximated well by a normal
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distribution (large sample sizes n), with mean S and variance 2S given by:
S = 0, 2S =
n(n 1)(2n + 5)
m
i=1
ti(i)(i 1)(2i + 5)
/18 (3)
This equation yields the variance of S with a correction for ties in data, with ti denotingthe number of ties of extent i. The standard normal variate is used for hypothesis testing,called the MK trend test statistic Z.
Z =
S1S
, if S < 0
0, if S = 0S+1S
, if S < 0.(4)
For a two-tailed test, the null hypothesis is rejected at significance level (Type I error) if
|Z| > Z/2, where Z/2 is the value of the standard normal distribution with an exceedanceprobability /2. Relative frequencies presented in the results section are obtained simplyby dividing the number of Z values for which |Z| > Z/2 applies by the total number ofstations. Low and high flows are reported separately. So, the relative frequency for a givenflow quantile indicates the percentage of stations that prsent a statistical significant trendof of high or low flows.
3.2. Theil-Sen slope estimate
The TheilSen slope estimator is a method for robust linear regression that chooses themedian slope among all lines through pairs of two-dimensional sample points. It is anonparametric method suitable for a nearly linear trend [Helsel u. Hirsch (2002)], andit is more robust than the least-squares estimator because it is much less sensitive tooutliers, meaning that it can tolerate arbitrary corruption of up to 29.3% of the inputdata-points without degradation of its accuracy. It can be significantly more accurate thansimple linear regression and competes well against simple least squares even for normallydistributed data [Wikipedia] . The slope is computed between all pairs i of the variable x:
i =xj xkj k , with j > k (5)
(j = 2,...,n; k = 1,...,n 1)
where i = 1...N. For n values in the time series x this will result in N = n(n
1)/2
values of . The slope estimate b is the median of bi, i = 1...N.
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3.3. Spearman rank correlation
The nonparametric rank-based Spearman correlation coefficient was used to report theresults of correlation analyses. Spearmans is a nonparametric rank-based correlation
coefficient used to estimate the monotone association between two random variables. IfY tends to increase when X increases, the Spearman correlation coefficient is positive. IfY tends to decrease when X increases, the Spearman correlation coefficient is negative.When X and Y are perfectly monotonically related, the Spearman correlation coefficientbecomes 1. It is computed from the difference d between the ranks of independently sortedvariables x and y [Kottegoda (2008)] :
= 1 6n
i=1 d2
n(n2 1) (6)
Under the null hypothesis of no correlation between x and y, the distribution of can be
approximated by a normal distribution with mean and variance 2
given by:
= 0, 2 = 1/(n 1) (7)
The random variables x and y are considered correlated at the significance level if|| > Z/2/
n 1 for a two-tailed test. = 0.1 was chosen for the analysis.
The causal aspects of identified trends in streamflow were investigated by correlationanalyses with 2 basin attributes: mean altitude of the basin and percentage of glaciercover.
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4. Results
The main results are reported in three sections. First, trends in streamflow are analysedfor different seasons and quantiles. Then, differences between groups with different station
altitudes and glacier cover are investigated. Thereafter, relationships between trends andbasin attributes are explored. Ultimately, some open questions are identified and discussedbriefly.
4.1. Trends
As pointed out earlier, choice of study period length is important because it has an impacton trend identification. If a large scale periodic behaviour is present in the records, thelength of analysis period should be chosen in a way that it spans one or more cyclesof this process. A 20 year period is assumed to contain low and high flow periods andtherefore identitified trends should not result from lowfrequency largescale behaviour inthe recorded data. Also, as can be seen in the graphs below, changes in runoff have astrong seasonal dependence and should therefore be considered separately.
Mann-Kendall
Relative frequencies of high and low flows were investigated. In figure 3 up and downtrends are shown for every season and period.
Spring: In the first period high flows are relatively frequent. Up to 40% of the stationsmanifest high flows for all quantiles. However, in the following two periods the frequenciesof high flows exhibit a subsiding development, especially for the lower quantiles. On theother hand, frequencies of low flows tend to increase over the three periods. Still, in
the most recent period quantiles above the median flow (q50) dont display statisticallysignificant low flows.
Summer: In this season there is little change over all periods, except for the frequenciesof low flows from 1980-2000. It seems that the summer of this period had particularlyfrequent low flows. Taken aside this fact, there is no strong significant up- or downwardtrend indicated by the MannKendall test.
Autumn: Autumn shows a similar picture as summer, with the difference that in thisseason an increase of frequent low flows occurs in the last period. Interestingly, the fre-quencies of low flows for the middle period dont follow those of the previous season. Even
high flows frequencies are more numerous after a relative dry summer.
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(a) Spring (b) Summer
(c) Autumn (d) Winter
Figure 3: Relative frequencies of high( +) and low(-) flows over all stations for all quantilesand for every period.
Winter: The first two periods reveal a rising number of high flows in winter. And yet,the last period presents the opposite situation. Frequencies of low flows have increasedconsiderably whereas high flows have practically vanished. This can be an indication of animportant shift of streamflow regime for the winter season.
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Theil-Sen slope estimate
Results for the Theil-Sen slope estimate for each season are shown below in figure 4.
(a) Spring (b) Summer
(c) Autumn (d) Winter
Figure 4: Slope estimate for all quantiles and for every period.
Spring: In the first period (1970-1990) spring flows show an increasing trend for all stream-flow quantiles. The two following periods also demonstrate an increasing trend, but of lowermagnitude. The other 2 periods show a reduced increase and even a decrease for the lowerquantiles.
Summer: Summer flows clearly exhibit decreasing trends in all periods and for all quan-
tiles, except for the maximum flow in the last period. In general the maximum flow insummer is due to heavy rainstorm events, so for the overall picture one can argue thatsummer flows are actively decreasing.
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Autumn: Autumn flows present relatively small changes in the first two periods. Again,there is a significant decrease in the most recent period. Put another way, this most likelyis an indication of a change in the runoff regime.
Winter: Winter season pictures a faint upward trend in the first two periods for all quan-tiles but maximum flow. Similarly to autumn, the trend is inverted in the last period andfor all quantiles (including maximum flow). Indeed, even the maximum flows in winter havesubstantially fallen from an extreme upward trend to a high decreasing trend. Accordingly,this again gives reason to presume a change in the winter streamflow regime.
Frequencies and magnitude
Looking at both frequency and magnitude together, the following can be said:
Spring flows show an increasing trend in both the MannKendall test and the slopeestimate. Moreover both also signal a subsiding development of this trend.
The MK test suggests that in summer, occurrence of high and low flows are moreor less balanced in every period (except for low flows in the middle period), but theslope estimate clearly reveals a decreasing trend.
In summer period from 1990-2010, the maximum flow has a substantial increase butwith a relative low frequency. Also, the frequencies of low flows are higher than thoseof high flows (except for qMIN, q10, q20). In each period low flows outnumber highones in summer, yielding a decreasing trend in runoff.
A clear change is noticeable for the most recent period in both MK test and Theil-Sen estimate. In other words, frequencies of low flows have risen and slope estimates
sketch out a decrease in flow magnitude over all quantiles.
Trends of streamflow in winter trace a similar, maybe even more pronounced, pictureas in autumn. In this season, from 1990-2010, not only frequencies of low flows haverisen, but frequencies of high flows have fall at the same time. Also the slope estimatehas switched from a weak increasing to a decreasing trend.
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4.2. Differences in altitude
For the period from 1990-2010, differences according to station altitude were analysed interms of slope (fig. 5) and relative frequency (fig. 6). To lower data load only two runoff
quantiles were looked at, namely q50 and q90.
Figure 5: Slope estimate [mm/season] and standard deviation for 50- and 90-percent quan-tiles grouped according to altitude for the period 1990-2010.
In spring, all 3 groups show an increasing slope. The summer season is most heteroge-neous with decreasing trends for low and high altitude stations, but an increasing slope forstations located between 1000m and 2000m. Autumn and winter both signal a decreasingtrend for both quantiles. These graphs also show that if a trend is visible (increases ordecreases), it tends to be a more pronounced for the higher quantile q90 (except for sum-mer). While this is true, there is no clearly discernible trend related to the mean elevation
of the watershed when looking at both quantiles.
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Comparing the slope trends with the relative frequencies of high and low flows, revealsthat the trends (slopes) found are endorsed by the Mann-Kendall test. Where springdisplays a positive trend for every altitude, high flows are common whereas low flows arelacking. The previously identified decreasing slope in autumn is matched by frequent low
flows. Particularly in winter for the 90 percent quantile, where slopes are slightly falling,low flows are quite frequent. This indicates that large runoff (q90) in winter is decreasingin magnitude and occur more seldom. To sum up, the mean altitude of a watershed doesnot play a significant role for streamflow regime alteration. Stations from all three altitudegroups exhibit similar behaviour when compared to each other.
Figure 6: Relative frequencies for 50- and 90-percent quantiles grouped according to alti-tude for the period 1990-2010.
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Glacier presence
To further investigate any relation between basin attributes and change in runoff regime,station records were divided into 2 groups depending on whether they presented glacier
cover or not. For these two groups, only the frequencies of high and low flows were consid-ered. The results are shown in figure 7 .
Figure 7: Relative frequencies for 50- and 90-percent quantiles grouped according to glaciercover for the period 1990-2010.
Relative frequencies from both groups coincide most often. In summer, stations with noglacier dont display any trend. In winter stations with glacier cover indicate a decreasingtrend for both quantiles, whereas the other group only exhibits a downward trend for q90.This means that basins with glaciers are facing overall frequent low flows, while basinswithout only experience this trend for large runoff. The median flow of the latter stations
is undisturbed. As seen earlier with elevation, no obvious relation of trend with glacierpresence is detectable.
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4.3. Correlation with basin attributes
In the graphs below (figure8) it is clear that correlation exists, but depends on season andquantile. However for smaller quantiles in winter there mostly is no statistically significant
correlation between mean basin altitude and estimated slope. From the methods section,one can calculate that for a 10% significance level and 39 stations, basin attributes andtrend are considered correlated if || > 0.27.
(a) (b)
Figure 8: Spearman rank correlation coefficients for mean basin altitude and estimatedslope (a) and MK Z statistic (b)
Correlation with estimated slope Positive correlation can be seen for high quantiles inWinter. Summer shows a negative correlation for moderate flows. Lower quantiles correlatenegatively for autumn. Spring has no proper tendency.
Correlation with Mann-Kendall Z statistic No really significant correlation can be seenfor all quantiles in Winter. The other three seasons are similar to the correlation with esti-mated slopes. In summer altitude correlates for moderate flows. Lower quantiles correlate
well for autumn. Again, spring has no clear tendency, displaying positive and negativecorrelations both for high and low flows.
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The Spearman rankbased correlation was also computed for glacier cover.Those corre-lation charts between glacier cover and streamflow trends can be found in appendix A.3.Results are comparable to those of mean basin altitude.
4.4. Open Quetions
As stated earlier, there seems to be a change in streamflow regime in at least 2 out of 4seasons (autumn and winter), especially for when comparing the most recent period withthe two previous ones. Now that changes have been identified, the question arises whatthese changes are due to and if in future these shifts will also be detectable in spring andsummer. Several things have to be investigated:
The assumption that a 20 year period sufficiently captures any large-scale periodicityshould be investigated. As pointed out by (P Pekarova, 2006) dry cycles of 13.5 and28-29 years have been identified (see also P Pekarova (2003)).
Another issue is to assert that these changes are not due to anthropogenic factorsnor emphasised by these. It is arguably nearly impossible to exclude anthropogenicinfluences altogether. If land use (and therfore land cover) changes in some of theanalysed basins this can have influenced the streamflow regime. Also changes in thefluvial systems should be taken into account. The time scale, on which these effectsoccur from external factors, could give an indication on whether they influence trendsor not.
we expect that most of the (natural) watershed changes occur on much longer timescalesthan those studied here, we recognise that they do contribute to hydrological vari-ability
Precipitation and air temperature data (focussing on days with minimum daily tem-perature above melting point) might explain some of the observed trends. Do changesin runoff properly reflect the input to a rainfall-runoff system, namely precipitation.
Changes in net glacier balance should be analysed together with identified trendsto assess whether there is a relationship between both that can be due to climatechange. For instance, glacier retreat will have an impact on land cover which againwill impact runoff.
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23 Streamflow Trends in Switzerland
5. Conclusions
This project work presents a statistical analysis of trends in mean daily streamflow recordsfrom 39 watersheds in Switzerland with a mostly undisturbed runoff regime for three
study periods (1970-1990, 1980-2000 and 1990-2010). Estimate of trend magnitude andstatistically significant trends were computed for each station on a seasonal basis andfor different streamflow quantiles. Identified trends in streamflow were correlated withwatershed attributes. The main conclusions are as follows:
Trends are present in every period as well for high and low flows. Magnitude dependson period and season of interest.
Particularly the last period (1990-2010) experiences a significant increase of lowerflows in Winter for every quantile. This suggests that winters are becoming increas-ingly dryer over the last 20 years.
In the winter season there is a considerable shift of frequent high flows to frequentlow flows in the last period of analysis (1990-2010).
The increasing trend of Spring flows is experiencing a decaying development over thethree analysed periods.
Summer flows exhibit a decreasing trend, particularly in magnitude. Autumn also reveals a shift in the last period. A decreasing trend in magnitude
matches an increase of statistical significant low flows from 1990-2010.
Winter flows also show a substantial shift in the last period similar to the autumnseason. In Addition to a rising number of low flows, the season presents only veryfew high flows.
There was no discernible dependence of trends related to the mean elevation of theanalysed watersheds.
Basins lacking presence of glacier dont show any trend. Particularly in winter medianflow of watersheds without glacier remains unchanged, while basins with glaciers facedownward trends for both q50 and q90. This trend should be followed closely if itpersists, because it can give an indication on what is happening to precipitation inhigher altitudes.
Correlation between mean watershed elevation and trends is strongly dependent on
season and quantile. No significant correlation was found in spring. Autumn andsummer show negative correlation for low flows, resp. moderate flows. In winter highflows show a good correlation with magnitude of trend (estimated slope).
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24 Streamflow Trends in Switzerland
The altitude groups followed the same trend patterns as the ones found when com-puting trends from all the available stations.
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25 Streamflow Trends in Switzerland
6. Acknowledgements
Thanks for the data I received from the Federal Office for the Environment (FOEN orBAFU in german).
Thanks to my supervisor Dr. Peter Molnar, who patiently guided me through this projectwork.Special Thanks to the 2 anonymous reviewers, who helped to improve this report.
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26 Streamflow Trends in Switzerland
References
[Aschwanden 1985] Aschwanden, Weingartner R. H.: Runoff Regimes in Switzerland.Pub. Gewasserkunde, 1985
[D. P. Lettenmaier 1991] D. P. Lettenmaier, Eric F. W. JAMES R. WALLIS W. JAMESR. WALLIS: A Daily Hydroclimatological Data Set for the Continental United States.In: WATER RESOURCES RESEARCH (1991)
[Helsel u. Hirsch 2002] Helsel, D.R. ; Hirsch, R.M.: Statistical Methods in WaterResources. U.S. GEOLOGICAL SURVEY, 2002
[Hess 2001] Hess, Iyer H. Malm W. A.: Linear trend analysis: a comparison of methods.In: Atmospheric Environment (2001), 10
[Kottegoda 2008] Kottegoda, Rosso R. N.T.: Statistics, Probability, and Reliability forCivil and Environmental Engineers. Bd. 2nd edition. Wiley-Blackwell, 2008
[M. Beniston u. Marinucci 1994] M. Beniston, F. G. M. Rebetez R. M. Rebetez ; Mar-inucci, M. R.: An Analysis of Regional Climate Change in Switzerland. In: Theoreticaland Applied Climatology (1994)
[M.-V. Birsan 2005] M.-V. Birsan, P. Burlando M. P. P. Molnar M. P. Molnar: Streamflowtrends in Switzerland. In: Journal of Hydrology (2005)
[P Pekarova 2003] P Pekarova, J. P. P. Miklanek M. P. Miklanek: Spatial and temporalrunoff oscillation analysis of the main rivers of the world during the 19th20th centuries.In: Journal of Hydrology (2003)
[P Pekarova 2006] P Pekarova, J. P. P. Miklanek M. P. Miklanek: Long-term trends andrunoff fluctuations of European rivers. In: Climate Variability and ChangeHydrologicalImpacts (2006)
[Pavel Ya. Groisman u. Karl 2001] Pavel Ya. Groisman, Richard W. K. ; Karl,Thomas R.: Heavy Precipitation and High Streamflow in the Contiguous United States:Trends in the Twentieth Century. In: Bulletin of the American Meteorological Society(2001)
[Wikipedia ] Wikipedia: Wikipedia. http://de.wikipedia.org, Abruf: 05. Dec 2011
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A. Appendix A
A.1. Stations
A.1.1. Basin Attributes
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!"#$%&%'
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ID
NEW_ID
AREA
K-Gravelius
ALTITUDE
SLO
PE
RIV_DENS
MEAN_CN
SOIL
%_ROCK
%GLA
CIER
PREC_ANN
833
2312
48.
5
1.
979
473
2.
6
1406
70.
4
93
0
0
1011
915
2202
261
1.
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585
13
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1223
71.
9
71
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1
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528
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9
2.
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648
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1
86
0.
3
0
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549
2132
342
2.
258
649
11
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2522
69.
5
82
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31 Streamflow Trends in Switzerland
A.2. Results
A.2.1. Slope estimate results
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readstations available
spring summer autumn winter 39 44
qmin 0.85 -1.88 -0.45 0.26
q10 1.28 -1.90 -0.40 0.19
q20 1.46 -1.37 -0.41 0.18
q30 1.67 -0.89 -0.37 0.09
q40 1.90 -1.02 -0.19 0.04
q50 1.74 -0.43 0.14 0.03
q60 1.70 0.07 0.42 0.17
q70 2.78 0.30 0.94 0.57
q80 5.28 -0.17 -0.34 1.13
q90 6.53 -0.08 -0.81 1.96
qmax 10.13 -7.40 1.82 20.36
spring summer autumn winter 39 51
qmin 0.42 -0.16 0.66 0.06q10 0.54 -0.26 0.80 0.21
q20 0.60 -0.28 0.82 0.18
q30 0.14 -1.15 0.87 0.25
q40 -0.23 -2.11 0.88 0.36
q50 -0.62 -3.31 0.89 0.42
q60 0.15 -4.51 0.40 0.42
q70 2.19 -6.06 -0.42 0.58
q80 2.19 -7.99 -0.40 0.66
q90 1.15 -8.96 1.04 0.84
qmax 5.12 -4.47 7.88 5.74
spring summer autumn winter 39 48
qmin -0.58 0.95 -0.27 -0.22
q10 -0.69 0.57 -0.39 -0.25
q20 -0.21 0.00 -0.56 -0.22
q30 0.38 -0.70 -0.73 -0.26
q40 1.10 -1.09 -1.00 -0.33
q50 1.68 -1.51 -1.57 -0.54
q60 2.50 -1.68 -2.09 -0.64
q70 1.89 -1.78 -3.16 -0.94
q80 3.19 -1.79 -3.83 -1.53q90 3.57 -0.62 -5.43 -2.39
qmax 12.55 7.03 -9.92 -10.32
1970-1990
1980-2000
1990-2010
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33 Streamflow Trends in Switzerland
A.2.2. Mann-Kendall relative frequency results
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35 Streamflow Trends in Switzerland
A.2.3. Altitude groups results
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39 Streamflow Trends in Switzerland
A.2.4. Glacier cover results
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spring
summer
autumn
winter
spring
summer
autumn
winter
qmin
-0.
10
0.
90
0.
09
0.
16
-0.
98
1.
00
-0.
58
-0.
55
q10
-0.
14
1.
08
-0.
09
0.
08
-1.
16
0.
14
-0.
64
-0.
53
q20
0.
47
1.
22
-0.
19
0.
12
-0.
79
-1.
06
-0.
88
-0.
52
q30
0.
93
0.
99
-0.
46
0.
07
-0.
09
-2.
15
-0.
96
-0.
55
q40
1.
35
0.
65
-0.
73
-0.
01
0.
88
-2.
58
-1.
22
-0.
61
q50
1.
95
-0.
04
-1.
36
-0.
22
1.
45
-2.
77
-1.
76
-0.
81
q60
2.
74
-0.
60
-2.
37
-0.
38
2.
29
-2.
61
-1.
84
-0.
86
q70
3.
26
-0.
89
-3.
59
-0.
78
0.
71
-2.
54
-2.
79
-1.
07
q80
4.
68
-0.
89
-4.
84
-1.
75
1.
90
-2.
56
-2.
97
-1.
34
q90
5.
61
0.
06
-7.
79
-3.
36
1.
81
-1.
20
-3.
42
-1.
55
qmax
10.
27
13.
79
-10.
00
-
16.
44
14.
50
1.
24
-9.
85
-5.
08
1990-2010
noglacier
glacier
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qmin
6%
17%
0%
48%
qmin
11%
0%
19%
0%
q10
6%
11%
0%
38%
q10
28%
0%
19%
5%
q20
6%
11%
0%
33%
q20
22%
0%
5%
14%
q30
11%
6%
5%
10%
q30
6%
0%
0%
14%
q40
17%
0%
24%
5%
q40
11%
0%
5%
19%
q50
28%
0%
33%
5%
q50
0%
0%
5%
29%
q60
39%
0%
38%
0%
q60
0%
0%
5%
19%
q70
28%
0%
5%
0%
q70
0%
0%
5%
19%
q80
44%
0%
10%
0%
q80
0%
0%
5%
14%
q90
17%
0%
5%
0%
q90
0%
6%
5%
10%
qmax
11%
0%
33%
0%
qmax
0%
6%
10%
10%
qmin
6%
0%
0%
24%
qmin
11%
11%
5%
29%
q10
6%
6%
0%
29%
q10
6%
6%
5%
38%
q20
6%
0%
0%
24%
q20
6%
11%
5%
29%
q30
0%
11%
0%
33%
q30
6%
0%
5%
29%
q40
6%
22%
0%
24%
q40
6%
6%
0%
33%
q50
0%
22%
0%
38%
q50
6%
6%
0%
43%
q60
0%
33%
0%
29%
q60
6%
6%
0%
38%
q70
0%
33%
0%
38%
q70
0%
11%
0%
48%
q80
0%
50%
0%
29%
q80
0%
28%
0%
48%
q90
0%
39%
0%
19%
q90
0%
39%
0%
43%
qmax
0%
33%
5%
24%
qmax
0%
44%
0%
43%
SPRING
SUMMER
AUTUMN
WINTER
1990-2010
1990-2010
1990-2010
1990-2010
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42 Streamflow Trends in Switzerland
A.2.5. Spearman rank correlation results
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spring summer autumn winter
qmin -0.14 -0.31 -0.06 0.30 1970
q10 -0.27 -0.24 -0.04 0.36 1990
q20 -0.26 0.06 0.07 0.26
q30 -0.25 0.19 0.15 0.32
q40 -0.31 0.16 0.23 0.39
q50 -0.32 0.21 0.30 0.39
q60 -0.26 0.22 0.28 0.22
q70 -0.10 0.24 0.29 -0.18
q80 0.11 0.19 0.18 -0.39
q90 0.04 0.24 0.12 -0.69
qmax -0.41 0.28 0.02 -0.72
qmin 0.32 0.19 0.54 0.32 1980
q10 0.39 0.17 0.33 0.26 2000
q20 0.39 0.20 0.25 0.33
q300.42 0.07 0.16 0.21
q40 0.50 -0.05 0.03 0.18
q50 0.57 -0.09 -0.12 0.27
q60 0.54 -0.17 -0.29 0.39
q70 0.68 -0.33 -0.40 0.36
q80 0.70 -0.59 -0.36 0.31
q90 0.69 -0.52 -0.16 0.20
qmax 0.40 -0.25 -0.01 -0.43
qmin -0.10 0.15 -0.38 -0.25 1990
q10 -0.27 -0.06 -0.41 -0.15 2010
q20 -0.46 -0.27 -0.50 -0.12q30 -0.36 -0.36 -0.37 -0.09
q40 -0.20 -0.38 -0.34 -0.08
q50 -0.18 -0.38 -0.27 -0.04
q60 -0.02 -0.35 -0.08 -0.01
q70 -0.29 -0.32 0.03 0.14
q80 -0.10 -0.20 0.09 0.39
q90 -0.14 -0.09 0.17 0.51
qmax 0.28 -0.26 -0.12 0.49
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spring summer autumn winter
qmin 0.06 -0.17 0.03 0.30 1970
q10 -0.08 -0.02 0.02 0.27 1990
q20 -0.17 0.19 0.10 0.20
q30 -0.27 0.22 0.20 0.23
q40 -0.32 0.22 0.34 0.21
q50 -0.34 0.23 0.30 0.20
q60 -0.22 0.22 0.21 0.17
q70 0.05 0.20 0.14 0.09
q80 0.26 0.18 0.13 0.04
q90 0.07 0.31 0.15 -0.14
qmax -0.26 0.30 -0.02 -0.45
qmin 0.43 0.24 0.50 0.17 1980
q10 0.56 0.14 0.35 0.19 2000
q20 0.56 0.10 0.21 0.17
q300.53 -0.01 0.15 0.13
q40 0.56 -0.04 0.05 0.18
q50 0.61 -0.07 -0.17 0.29
q60 0.70 -0.16 -0.30 0.45
q70 0.81 -0.36 -0.44 0.53
q80 0.82 -0.57 -0.41 0.50
q90 0.80 -0.52 -0.23 0.45
qmax 0.53 -0.38 0.05 0.12
qmin -0.17 -0.10 -0.42 -0.32 1990
q10 -0.53 -0.22 -0.41 -0.18 2010
q20 -0.65 -0.38 -0.49 -0.20q30 -0.50 -0.44 -0.39 -0.16
q40 -0.24 -0.35 -0.33 -0.19
q50 -0.07 -0.36 -0.25 -0.20
q60 -0.01 -0.29 0.09 -0.29
q70 -0.52 -0.16 0.21 -0.17
q80 -0.39 -0.03 0.22 0.02
q90 -0.35 0.01 0.23 0.20
qmax 0.55 -0.33 -0.04 0.24
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spring summer autumn winter
qmin -0.20 0.26 -0.33 -0.23 1990
q10 -0.22 -0.15 -0.35 -0.21 2010
q20 -0.35 -0.60 -0.37 -0.17
q30 -0.36 -0.66 -0.25 -0.13
q40 -0.28 -0.66 -0.28 -0.13
q50 -0.35 -0.56 -0.42 -0.18
q60 -0.22 -0.45 -0.25 -0.18
q70 -0.22 -0.37 -0.16 -0.10
q80 -0.02 -0.28 -0.09 0.09
q90 -0.21 -0.29 0.16 0.20
qmax 0.15 -0.28 0.01 0.24
qmin -0.35 -0.05 -0.36 -0.29 1990
q10-0.44 -0.36 -0.39 -0.29
2010q20 -0.48 -0.57 -0.47 -0.26
q30 -0.51 -0.63 -0.31 -0.23
q40 -0.40 -0.59 -0.25 -0.25
q50 -0.34 -0.48 -0.34 -0.33
q60 -0.15 -0.39 -0.09 -0.46
q70 -0.33 -0.23 0.02 -0.40
q80 -0.13 -0.16 0.08 -0.33
q90 -0.29 -0.17 0.23 -0.13
qmax 0.41 -0.30 0.12 -0.21
correlationslope-glaciercover
correlationZ-glaciercover
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46 Streamflow Trends in Switzerland
A.3. Additional Figures
Figure 9: Representative Discharge [mm/season] for all season of q90 streamflow averagedover all stations.
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47 Streamflow Trends in Switzerland
Figure 10: Representative discharge [mm/year] for all season of q90 streamflow averagedover all stations and grouped by station altitude.
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48 Streamflow Trends in Switzerland
Figure 11: Estimated slopes [mm/season] and standard deviation for 50- and 90-percentquantiles grouped according to glacier cover for the period 1990-2010.
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49 Streamflow Trends in Switzerland
(a)
(b)
Figure 12: Spearman rank correlation coefficients of relative glacier cover and estimated
slope (a) and MK Z statistic (b)
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50 Streamflow Trends in Switzerland
B. Appendix B
B.1. Main Matlab Program for Mann-Kendall Theil-Sen
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1
%
main
file
%select
range
of
records
by
setting
star
t_year
and
end_year
%selct
input
files
by
editing
file_paths
.m
(enter
paths
to
files
&
file
%names)
%%
path
name
vectors
%run
file_paths.m
to
get
file
names
&
pa
ths
file_paths_all
%%
read
data
display('start
read
data');
start_year
=
1990;
end_year
=
2010;
%group
stations
according
to
either
alti
tude
or
slope
or
glacier
cover:
1
=
yes,
0=no
altitude
=
[0;
1000;
2000];
%get
calc
ulations
depending
on
altitude
of
stations
slope
=
[0;
16;
28];
%get
calc
ulations
depending
on
slope
of
stations
glacier
=
[1;
0.1];
%get
calcu
lations
depending
on
slope
of
stations
skipped
=
[1
2
3];
%
stations
where
data
range
is
not
available
for
given
start
&
end
year
station_
list
=
[];
%
stations
with
avail
able
data
%read
data
from
all
stations
with
record
ed
data
for
selected
period
k=1;
for
i=1:length(file_paths)
%read
data
from
file
[runoff_
daily_
date
st_range
st_numbe
r
st_name]
=
read_
data(file_paths{i});
%check
if
data
available
before
sele
ction
if
(start_year
st_range(2))
skipped
=
[skipped
;
st_number
s
t_range];
continue
else
runoff_
daily(:,k)
=
select_
data(runo
ff_
daily_
date,
start_year,
end_year);
station_
list
=
[station_
list;
st_num
ber];
k=k+1;
end
end
%read
basin
attributes
of
stations
[num,txt,raw]
=
xlsread('BasinAttributes
.xls','BasinAttributes','B2:C50');
basin_attr
=
[num(:,2:3)
num(:,5:6)
num(
:,11)];%
get
station
number,
area(km^2),
altitude(m),
slope(%)
%find
basin
area
for
every
station
and
i
nsert
in
station_
list
for
i=1:length(station_
list)
for
j=1:length(basin_attr)
if
(station_
list(i)
==
basin_att
r(j,1))
station_
list(i,2:5)
=
basin_
attr(j,2:5);
end
end
%add
missing
basin
area
stations
to
skipped
stations
list
if
(station_
list(i,2)
==
0)
skipped
=
[skipped
;
station_
lis
t(i,1)
station_
list(i,2)
1];
end
end
display('end
read
data');
%%
process
data
mann
kendall
(Z-value)
a
nd
slope
display('START
process
data');
%Division
into
seasons
2
[lengtth
wi
dtth]
=
size(runoff_
daily);
for
i=1:wid
tth
%for
every
station
%select
one
station
add
date
for
season
division
station
(1:lengtth,1)
=
runoff_
daily(1:lengtth,i);
station
=
add_
date(station,
start_year,
end_year);
%divide
runoff
according
to
season
[spring
,
summer,
autumn,
winter]
=
season_
div(station);
%calcul
ate
quantiles
q_sprin
g
=
quant_calc(spring(2:93,:));
q_summe
r
=
quant_calc(summer(2:93,:));
q_autum
n
=
quant_calc(autumn(2:92,:));
q_winte
r
=
quant_calc(winter(2:92,:));
for
j=1
:1:11
%Ma
nn-Kendall
test
spr
ing_mk_test(j,i)
=
mann_
kendall_test(q_spring(j,:
));
sum
mer_mk_test(j,i)
=
mann_
kendall_test(q_summer(j,:
));
aut
umn_mk_test(j,i)
=
mann_
kendall_test(q_autumn(j,:
));
win
ter_mk_test(j,i)
=
mann_
kendall_test(q_winter(j,:
));
%Th
eil-Sen
slope
spr
ing_ts_slope(j,i)
=
theil_sen_slope(q_spring(j,:)
);
sum
mer_ts_slope(j,i)
=
theil_sen_slope(q_summer(j,:)
);
aut
umn_ts_slope(j,i)
=
theil_sen_slope(q_autumn(j,:)
);
win
ter_ts_slope(j,i)
=
theil_sen_slope(q_winter(j,:)
);
end
end
clear
sprin
g
summer
autumn
winter
clear
q_spr
ing
q_summer
q_autumn
q_winter
clear
stati
on
runoff_
daily_
date
runoff_
daily
%%
calculat
e
frequencies
of
stat.
significant
values
[spring_rel
Freq(:,1),
spring_relFreq(:,2)]
=
freq_Z(spring_m
k_test,0.1);
[summer_rel
Freq(:,1),
summer_relFreq(:,2)]
=
freq_Z(summer_m
k_test,0.1);
[autumn_rel
Freq(:,1),
autumn_relFreq(:,2)]
=
freq_Z(autumn_m
k_test,0.1);
[winter_rel
Freq(:,1),
winter_relFreq(:,2)]
=
freq_Z(winter_m
k_test,0.1);
display('EN
D
process
data');
%%
convert
slopes
to
mm/season
and
calculate
b_mean
display('ST
ART
slope
data');
%
convertf
orm
m3/s
to
mm/season
with
bason
attributes
for
i=1:11
spring_
ts_slope(i,:)
=
spring_ts_slope(i,:)./
transpose(
station_
list(:,2))*3.6*24*92;
summer_
ts_slope(i,:)
=
summer_ts_slope(i,:)./
transpose(
station_
list(:,2))*3.6*24*92;
autumn_
ts_slope(i,:)
=
autumn_ts_slope(i,:)./
transpose(
station_
list(:,2))*3.6*24*91;
winter_
ts_slope(i,:)
=
winter_ts_slope(i,:)./
transpose(
station_
list(:,2))*3.6*24*90;
end
%
remove
in
f
values
skipped_
bas
inatt_missing
=
[];
[le
wi]
=s
ize(spring_ts_slope);
for
i=1:wi
if
(
ab
s(spring_ts_slope(1,i))
==
inf)
spr
ing_ts_slope(:,i)
=
NaN;
sum
mer_ts_slope(:,i)
=
NaN;
aut
umn_ts_slope(:,i)
=
NaN;
win
ter_ts_slope(:,i)
=
NaN;
8/23/2019 Project Work Kevin Mersch Report
52/56
3
%make
list
of
missing
basin
attr
ibutes
skipped_
basinatt_missing
=
[skip
ped_
basinatt_missing
;
station_
list(i,1:2)];
end
end
display('END
slope
data');
%%
group
according
to
stations
group_station_
list
=
ones(length(station
_list),1);
%if
no
groups
if
(altitude(1)
==
1)
%if
grouped
by
ele
vation
group_station_
list
=
group_stations(
station_
list,
altitude);
elseif
(slope(1)
==
1)
%if
grouped
by
sl
ope
group_station_
list
=
group_stations(
station_
list,
slope);
elseif
(glacier(1)
==
1)
group_station_
list
=
group_stations(
station_
list,
glacier);
end
[m
n]
=
size(group_station_
list);
for
g=0:4:4*n-1
%for
different
groups
(start
with
0
so
g/4+1==1)
%mean
and
std
of
slope
over
all
stat
ions
%
g+1,+2,+3,+4
g=[1
2
3
4][5
6
7
8][
9
10
11
12]
%
g/4+1
g=[1][2][3][4]
%
2*g/4+1,+2
g=[1
2][3
4][5
6]
for
i=1:11
%b
slope_mean(i,g+1)
=
nanmean(
spr
ing_ts_slope(i,:).*
transpose(group_station_
list(:,g/4+1))
)
;
slope_mean(i,g+2)
=
nanmean(
sum
mer_ts_slope(i,:).*
transpose(group_station_
list(:,g/4+1))
)
;
slope_mean(i,g+3)
=
nanmean(
aut
umn_ts_slope(i,:).*
transpose(group_station_
list(:,g/4+1))
)
;
slope_mean(i,g+4)
=
nanmean(
win
ter_ts_slope(i,:).*
transpose(group_station_
list(:,g/4+1))
)
;
slope_stdev(i,g+1)
=
nanstd(
spr
ing_ts_slope(i,:).*
transpose(group_station_
list(:,g/4+1))
)
;
slope_stdev(i,g+2)
=
nanstd(
sum
mer_ts_slope(i,:).*
transpose(group_station_
list(:,g/4+1))
)
;
slope_stdev(i,g+3)
=
nanstd(
aut
umn_ts_slope(i,:).*
transpose(group_station_
list(:,g/4+1))
)
;
slope_stdev(i,g+4)
=
nanstd(
win
ter_ts_slope(i,:).*
transpose(group_station_
list(:,g/4+1))
)
;
%Z
[spring_relFreq(i,2*g/4+1),
spri
ng_relFreq(i,2*g/4+2)]
=
freq_Z(
spring_mk_test(i,:).*
transpose(
group_station_
list(:,g/4+1)),0.1
);
[summer_relFreq(i,2*g/4+1),
summ
er_relFreq(i,2*g/4+2)]
=
freq_Z(
summer_mk_test(i,:).*
transpose(
group_station_
list(:,g/4+1)),0.1
);
[autumn_relFreq(i,2*g/4+1),
autu
mn_relFreq(i,2*g/4+2)]
=
freq_Z(
autumn_mk_test(i,:).*
transpose(
group_station_
list(:,g/4+1)),0.1
);
[winter_relFreq(i,2*g/4+1),
wint
er_relFreq(i,2*g/4+2)]
=
freq_Z(
winter_mk_test(i,:).*
transpose(
group_station_
list(:,g/4+1)),0.1
);
end
end
display('END
grouping');
%%
spearman
rank
coefficient
%altitude
correlation
spearman_
b_altitude(:,1)
=
spearman_rho(
spring_ts_slope,
station_
list(:,3));
spearman_
b_altitude(:,2)
=
spearman_rho(
summer_ts_slope,
station_
list(:,3));
spearman_
b_altitude(:,3)
=
spearman_rho(
autumn_ts_slope,
station_
list(:,3));
spearman_
b_altitude(:,4)
=
spearman_rho(
winter_ts_slope,
station_
list(:,3));
4
%altitudec
orrelation
spearman_Z_
altitude(:,1)
=
spearman_rho(spring_mk_test,
stat
ion_
list(:,3));
spearman_Z_
altitude(:,2)
=
spearman_rho(summer_mk_test,
stat
ion_
list(:,3));
spearman_Z_
altitude(:,3)
=
spearman_rho(autumn_mk_test,
stat
ion_
list(:,3));
spearman_Z_
altitude(:,4)
=
spearman_rho(winter_mk_test,
stat
ion_
list(:,3));
%glacier
co
verage
correlation
spearman_
b_
glacier(:,1)
=
spearman_rho(spring_ts_slope,
stat
ion_
list(:,5));
spearman_
b_
glacier(:,2)
=
spearman_rho(summer_ts_slope,
stat
ion_
list(:,5));
spearman_
b_
glacier(:,3)
=
spearman_rho(autumn_ts_slope,
stat
ion_
list(:,5));
spearman_
b_
glacier(:,4)
=
spearman_rho(winter_ts_slope,
stat
ion_
list(:,5));
%glacier
co
verage
correlation
spearman_Z_
glacier(:,1)
=
spearman_rho(spring_mk_test,
stati
on_
list(:,5));
spearman_Z_
glacier(:,2)
=
spearman_rho(summer_mk_test,
stati
on_
list(:,5));
spearman_Z_
glacier(:,3)
=
spearman_rho(autumn_mk_test,
stati
on_
list(:,5));
spearman_Z_
glacier(:,4)
=
spearman_rho(winter_mk_test,
stati
on_
list(:,5));
display('EN
D
spearman');
%%
plotting
frequencies
%
%
figure;
%
%
subplot(2
,2,1);
%spring
%
spring_
fr
equencies
=
[frequencies_rel_max(:,1)
frequencie